The application relates to the field of process control engineering, and more particularly adaptive process control.
The present applicant""s previous U.S. Pat. No. 5,335,164 issued Aug. 2, 1994 and U.S. Pat. No. 5,687,077 issued Nov. 11, 1997, the contents of which are incorporated herein by reference, disclose methods and apparatus for adaptive control which use orthonormal Laguerre functions to model the process to be controlled. Such methods have proven useful for modelling and controlling inherently stable systems which eventually settle at a steady state, also referred to as self-regulating systems. However these methods are not suitable for xe2x80x9cmarginally stablexe2x80x9d or unstable systems. A xe2x80x9cmarginally stablexe2x80x9d system is a system which is only stable for a certain control input. An unstable system is one which cannot be made stable by any control input. An example of a marginally stable system is a leaky water tank. A control input which matches the rate of leakage results in a stable system, but an input greater or less than the rate of leakage results in either emptying or overflow of the tank. Obviously many important systems, such as those involving an energy input such as heat to a system, are marginally stable. Previous methods have difficulty modelling marginally stable systems because such systems have a process value y which goes to zero or infinity at every control input except the stable control input. For example, conventional Proportional-Integral-Derivative (PID) based loop controllers have difficulty controlling processes that involve the heating and cooling of a closed batch reactor.
There is therefore a need for a method of adaptive control which can model and control marginally stable systems.
The present invention provides a method and apparatus for adaptive control which models marginally stable systems by creating a reference or disturbance model to account for a constant slope of the process variable for different valves of the control input.